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5. * a be a primitive element of...
Consider the 2-error correcting RS code over GF(8). Let α be a primitive element of GF(8). (a) List the parameters of the code. Find the generator polynomial of the code. Encode the message [1 α α2 ]...
Consider the 2-error correcting RS code over GF(8). Let α be a primitive element of GF(8). (a) List the parameters of the code. Find the generator polynomial of the code. Encode the message [1 α α2 ] systematically. (b) List the parameters of the binary expanded code. Provide binary equivalents of the encoding above. (c) Decode the received word [0 1 α α2 α3 1 0].
Exercise 1 Let E, FCC and let E 2F be a field. (a) Without using the primitive element theorem, s...
Exercise 1 Let E, FCC and let E 2F be a field. (a) Without using the primitive element theorem, show that [E : FI < oo if and only if (Hint: Tower law → [F(01, , , , a.) : F1 < oo. For the other direction, use induction on IE、F) (b) Suppose that E F(a Show that E is normal if and only if for every E Flai, . . . , α.) for some on. . . ....
Problem (A1) (20 points): Huffman Coding Consider a message having the 5 symbols (A,B,C,D,E) with probabilities...
Problem (A1) (20 points): Huffman Coding Consider a message having the 5 symbols (A,B,C,D,E) with probabilities (0.1,0.1,0.2 ,0.2, 0.4), respectively. For such data, two different sets of Huffman codes can result from a different tie breaking during the construction of the Huffman trees. • Construct the two Huffman trees. (8 points) Construct the Huffman codes for the given symbols for each tree. (4 points) Show that both trees will produce the same average code length. (4 points) For data transmission...
Exercise 1 Assume that a binary symmetric channel is used in this question as shown in fig. 1 I-p...
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Exercise 1 Assume that a binary symmetric channel is used in this question as shown in fig. 1 I-p 0 0 Alice (encoder) Bob (decoder) 1 1-P Figure 1 The Binary symmetric channel where the probability of a bit being wrongly decoded by Bob is p i) Two codes are proposed: a...
Solve problem 2 using the priblem 1 . Question is taken from Ring theory dealing with ideals and ...
Solve problem 2 using the priblem 1 . Question is taken from
Ring theory dealing with ideals and generating sets for
ideals.
Problem 1. Suppose that R (R,+ Jis a commutative ring with unity, and suppose F- (a,,. , a } is a finite nonempty subset of R. Modify your proof for Problem 5 above to show that 7n j-1 Problem 2. Consider the set Zo of integer sequences introduced in Homework Problem 6 of Investigation 16. You showed that...
I am not sure how to do icu lact that thie muiiplication of matrices with real...
I am not sure how to do
icu lact that thie muiiplication of matrices with real coefficients is associative. 1. Show that every cyclic group is abelian. 2. Let m be an integer greater than 1. For any l e Z, let Im denote the remain- der of the division of I by m. Let: Zm = {0. 1, 2, . . . ,m-1)- on Zm as follows: Define a binary operation where + is the usual addition of integers....
Please answer the parts 6 and 7. Thank you. 2. In this problem, we will prove...
Please answer the parts 6 and 7. Thank you.
2. In this problem, we will prove the following result: If G is a group of order 35, then G is isomorphic to Zg We will proceed by contradiction, so throughout the following questions, assume that G is a group of order 35 that is not cyclic. Most of these questions can he solved independently I. Show that every element of G except the identity has order 5 or 7. Let...
The following table is partially filled. 0 1 4 0 Xi 4 D a) Explain why c[1,1] to c[1,5] and c[2,1...
The following table is partially filled. 0 1 4 0 Xi 4 D a) Explain why c[1,1] to c[1,5] and c[2,1] to c[5,1] are all 1s? b) Compute c[2,2], and which cell do you refer to when computing it? c) Compute c 2,31 and c[3,2], which cell do you refer to directly this time? d) Fill up the rest of the cells. Assume that you take c[i,j - 1] when there is a draw in line 11. (i.e., take the...
Problem 1 Given the OFDMA scheme with the following constraints, iA bandwidth of 5 MHz in)...
Problem 1 Given the OFDMA scheme with the following constraints, iA bandwidth of 5 MHz in) The channel spacing is 15 KHz and symbol duration-ios- i) The Cyclic Prefix (CP) for each symbol is 16.67pus long iv) The Time Division Multiplexing (TDM) frame duration is 10 ms Answer the following: How many subcarriers are available? How many symbols can be fit into one TDM frame? a) b) 2. The following table illustrates the operation of an FHSS system for one...
please solve the question completely and show the steps ... thumb up will be given 1....
please solve the question completely and show the steps ...
thumb up will be given
1. (3 points each) [CO: 11 a. Perform the number conversion (2101)s -6 binary equivalent of the Gray code numbers listed below in ascending order, ie, b. List all 4-bit from smallest to largest. (Hint: Use the mirroring technique.) Gray-Code Straight Binary Equivalent 0001 0011 0010 0110 0111 0101 0100 1100 1101 Perform the following binary multiplication: c. (1031)4 (1031)4 Perform the following base-3 addition:...
Exercise 1 Let E, FCC and let E 2F be a field. (a) Without using the primitive element theorem, show that [E : FI < oo if and only if (Hint: Tower law → [F(01, , , , a.) : F1 < oo. For the other direction, use induction on IE、F) (b) Suppose that E F(a Show that E is normal if and only if for every E Flai, . . . , α.) for some on. . . ....
Problem (A1) (20 points): Huffman Coding Consider a message having the 5 symbols (A,B,C,D,E) with probabilities (0.1,0.1,0.2 ,0.2, 0.4), respectively. For such data, two different sets of Huffman codes can result from a different tie breaking during the construction of the Huffman trees. • Construct the two Huffman trees. (8 points) Construct the Huffman codes for the given symbols for each tree. (4 points) Show that both trees will produce the same average code length. (4 points) For data transmission...
I need it urgently. Kindly provide me in neat and clean. Thanks
in advance.
This information is complete and if You think info is incomplete
than kindly mention.
Exercise 1 Assume that a binary symmetric channel is used in this question as shown in fig. 1 I-p 0 0 Alice (encoder) Bob (decoder) 1 1-P Figure 1 The Binary symmetric channel where the probability of a bit being wrongly decoded by Bob is p i) Two codes are proposed: a...
Solve problem 2 using the priblem 1 . Question is taken from
Ring theory dealing with ideals and generating sets for
ideals.
Problem 1. Suppose that R (R,+ Jis a commutative ring with unity, and suppose F- (a,,. , a } is a finite nonempty subset of R. Modify your proof for Problem 5 above to show that 7n j-1 Problem 2. Consider the set Zo of integer sequences introduced in Homework Problem 6 of Investigation 16. You showed that...
I am not sure how to do
icu lact that thie muiiplication of matrices with real coefficients is associative. 1. Show that every cyclic group is abelian. 2. Let m be an integer greater than 1. For any l e Z, let Im denote the remain- der of the division of I by m. Let: Zm = {0. 1, 2, . . . ,m-1)- on Zm as follows: Define a binary operation where + is the usual addition of integers....
Please answer the parts 6 and 7. Thank you.
2. In this problem, we will prove the following result: If G is a group of order 35, then G is isomorphic to Zg We will proceed by contradiction, so throughout the following questions, assume that G is a group of order 35 that is not cyclic. Most of these questions can he solved independently I. Show that every element of G except the identity has order 5 or 7. Let...
The following table is partially filled. 0 1 4 0 Xi 4 D a) Explain why c[1,1] to c[1,5] and c[2,1] to c[5,1] are all 1s? b) Compute c[2,2], and which cell do you refer to when computing it? c) Compute c 2,31 and c[3,2], which cell do you refer to directly this time? d) Fill up the rest of the cells. Assume that you take c[i,j - 1] when there is a draw in line 11. (i.e., take the...
Problem 1 Given the OFDMA scheme with the following constraints, iA bandwidth of 5 MHz in) The channel spacing is 15 KHz and symbol duration-ios- i) The Cyclic Prefix (CP) for each symbol is 16.67pus long iv) The Time Division Multiplexing (TDM) frame duration is 10 ms Answer the following: How many subcarriers are available? How many symbols can be fit into one TDM frame? a) b) 2. The following table illustrates the operation of an FHSS system for one...
please solve the question completely and show the steps ...
thumb up will be given
1. (3 points each) [CO: 11 a. Perform the number conversion (2101)s -6 binary equivalent of the Gray code numbers listed below in ascending order, ie, b. List all 4-bit from smallest to largest. (Hint: Use the mirroring technique.) Gray-Code Straight Binary Equivalent 0001 0011 0010 0110 0111 0101 0100 1100 1101 Perform the following binary multiplication: c. (1031)4 (1031)4 Perform the following base-3 addition:...
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